The Spectrum of the Hydrogen Atom

The Spectrum of the Hydrogen Atom - Michael Lin Partners...

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Michael Lin Tuesday Section Partners: Josh Narciso, Bryant Rolfe Due Date: 04/04/07 The Spectrum of the Hydrogen Atom Michael Lin The objective of this experiment was to observe the discrete light spectrum from a gas discharge lamp using a diffraction grating spectrometer. The wavelength of the light was calculated by observing the angular differences between monochromatic lines produced by the spectrometer. n i values (initial atomic shell) were determined for each wavelength. The n i value for the purple-blue spectral line was 4.85216 +/- 0.09243; for the blue-green line it was 3.76101 +/- 0.03370; for the dark red line it was 2.93120 +/- 0.01004. INTRODUCTION When large voltages are applied to gases, dielectric breakdown occurs, causing them to emit light. By using a spectrometer to observe the emitted light, monochromatic lines of different pure colors will occur on a dark background. Hydrogen gas emits four visible lines during its dielectric breakdown: red, green, blue, and violet. The spectrum of the hydrogen atom is therefore much less broad than the spectrum observed from visible light or sunlight. The color of light is related to its wavelength (visible) by the equation: 1/λ = R(1/2 2 – 1/n i 2 ) ; where R = 1.0974 * 10 7 m -1 Other spectral lines beyond visible wavelength can be described by the generalized formula: 1/λ = R(1/n f 2 – 1/n i 2 ) The production of visible spectral lines by atoms can be described by Bohr’s theory of valence electrons. In Bohr’s theory, valence electrons can be excited and jump between energy states. The drop of the electron between energy states after the excitation releases light to conserve energy, with the color being determined by the magnitude of the difference between the two states (wavelengths corresponding to energy difference). Bohr’s formula for the energy of the hydrogen atom’s quantum energy levels is: E n = -[me 4 /(8ε 0 2 h 2 )](1/n 2 ) Combined with Planck’s equation relating energy to wavelength yields the expression for the wavelength of light emitted during an atomic transition: 1/λ = [me 4 /(8ε 0 2 h 3 c)](1/n f 2 – 1/n i 2 ) Transmission gratings are used to decompose a spectrum into monochromatic lines. When a light beam incidents on a grating, each slit on the grating will diffract the beam into separate waves. The
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